Question

How to find the sum of the first 7 terms of the geometric sequence: 24, 12, 6, 3, ..... ?

Answer 1

See explanation below

Explanation:

In a geometric sequence, the sum of `n` terms is given by

`S_n=a_1(r^n-1)/(r-1)`

In our case we need to find the ratio. Obviously `r=1/2` and `a_1=24`, then applying formula

`S_7=24((1/2)^7-1)/(1/2-1)=47.625`

Answer 2

`S_7=381/8`

Explanation:

`"the sum to n terms of a geometric sequence is"`

`•color(white)(x)S_n=(a(1-r^n))/(1-r)`

`"where a is the first term and r the common ratio"`

`•color(white)(x)r=a_2/a_1=a_3/a_2=......=a_n/a_(n-1)`

`"here "a=24`

`"and "r=12/24=6/12=3/6=1/2`

`S_7=(24(1-(1/2)^7))/(1-1/2)`

`color(white)(xx)=(24(1-1/128))/(1/2)`

`color(white)(xx)=(24xx127/128)/(1/2)`

`color(white)(xx)=48xx127/128=6096/128=381/8`